Given a circle in which the width and height of an arc are given. The task is to find the radius of the circle with the help of the width and height of the arc.
Input: d = 4, h = 1 Output: The radius of the circle is 2.5 Input: d = 14, h = 8 Output: The radius of the circle is 7.0625
- Let the radius of the circle be r
- Let the height and width of the arc be h & d
- Now, the diameter DC bisects the chord AB in two halves, each having length d/2
- Also the diameter is divided by the chord in two parts, the part inside arc h and the remaining 2r-h
- Now from intersecting chords theorem,
h*(2r-h) = (d/2)^2
or, 2rh – h^2 = d^2/4
so, r = d^2/8h + h/2
- So, radius of the circle
Below is the implementation of the above approach:
The radius of the circle is 2.5
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